A181108 Array whose rows result from iterating an algorithm that carries the natural numbers to the lower Wythoff sequence.

1, 2, 1, 3, 3, 1, 4, 4, 3, 1, 5, 6, 4, 3, 1, 6, 8, 5, 4, 3, 1, 7, 9, 7, 5, 4, 3, 1, 8, 11, 9, 7, 5, 4, 3, 1, 9, 12, 10, 9, 7, 5, 4, 3, 1, 10, 14, 12, 11, 9, 7, 5, 4, 3, 1, 11, 16, 14, 12, 11, 9, 7, 5, 4, 3, 1, 12, 17, 16, 13, 12, 11, 9, 7, 5, 4, 3, 1, 13, 19, 17, 15, 13, 12, 11, 9, 7, 5, 4, 3, 1, 14, 21

Offset

1,2

Comments

Row 1: A000027 (natural numbers).

Row 2: A000201 (lower Wythoff sequence).

Limit-row: A003159.

Links

Table of n, a(n) for n=1..93.

Formula

To generate row n+1 from row n, let

(row n) = (s(1), s(2), s(3), ...)

(row n+1) = (t(1), t(2), t(3), ...)

Then for k=1,2,3,..., let

t(k) = least positive integer not yet in sequences t or u

u(k) = t(k) + s(k).

Example

Northwest corner:
1...2...3...4...5...6...7....8....9...
1...3...4...6...8...9...11...12...14...
1...3...4...5...7...9...10...12...14...
1...3...4...5...7...9...11...12...13...
To get row 2 from row 1:
s: 1...2...3...4...5....6....7...
t: 1...3...4...6...8....9....11...
u: 2...5...7...10..13...15...18...
To get row 3 from row 2:
s: 1...3...4...6....8....9....11
t: 1...3...4...5....7....9....10
u: 2...6...8...11...15...18...21

Crossrefs

Cf. A000201, A003159, A181109.

Sequence in context: A115131 A263916 A210258 * A211782 A211701 A183110

Adjacent sequences: A181105 A181106 A181107 * A181109 A181110 A181111

Keyword

nonn,tabl

Author

Clark Kimberling, Oct 03 2010

Status

approved